等价类空间中离散时间选举一排它混合模型的遍历性

利用李雅谱诺夫函数首先证明了等价类空间中离散时间非紧邻选举模型是正常返的,且首次击中D0时刻的阶为15/14,其次给出了等价类空间中离散时间非紧邻选举模型与排它过程的混合模型遍历性的一个判别准则,从而推广和改进了紧邻情形的相应结果.     

等价类空间中离散时间有限程排它过程的若干性质

本文利用李雅谱诺夫函数给出了等价类空间中离散时间有限程排它过程遍历、暂留的判别准则,推广、改进该模型在紧邻情形下的相应结果.     

等价类空间中一维有偏选举模型的刻画

本文利用李雅谱诺夫函数证明了等价类空间中的一维有偏选举模型是正常返的,且首次击中D0时刻的阶为32,从而推广了[4]中的部分结果.     

强零维度量空间的刻画

本文研究了强零维度量空间,借助点星弱邻域网刻画了强零维度量空间,获得了强零维度量空间等价于具有离散覆盖列的点星弱邻域网的非空正则空间,回答了葛英提出的一个问题.     

关于3—PBIB设计的构造

在本文中,我们利用V_n(F_q)中包含一个给定的m维子空间的m 1维子空间作为处理,以F_q上n×n非奇异交错矩阵的等价类作为区组,或以F_q~2上n×n非奇异Hermite矩阵的等价类作为区组,构作了一系列3-PBIB设计,并计算了它们的参数。     

离散型冲击折扣半马氏决策过程

本文讨论离散型冲击折扣半马氏决策过程，在建立模型后，我们将它化成了一个等价的离散时间马氏决策过程．     

跳过程的强遍历性

研究了一般状态空间跳过程的强遍历性,利用骨架链的方法,给出了强遍历性的几个等价条件,得到的结论类似于离散时间一般状态空间马氏链.     

二维非稳态对流扩散边界控制问题的简化算法

针对二维非稳态对流扩散边界控制问题计算量大的问题,提出了基于降阶模型的最优实时控制方法.利用POD(the Proper Orthogonal Decomposition)和奇异值分解以及Galerkin投影方法得到了具有高精度离散形式的状态空间降阶模型.在所得的降阶状态空间模型中,利用离散时间线性二次调节器方法设计出了最优控制器.对流-扩散过程的控制模拟结果说明了所提方法的有效性和准确性.     

拓扑空间的内部运算

讨论了拓扑空间上内部运算的性质,并对满足内部运算前三条性质的一类运算,引入一种等价关系,将这些运算进行等价分类,证明了每个等价类中的所有运算导出同一个拓扑,并进一步证明了每个等价类中仅有一个是内部运算且是等价类中的最小元.     

一维紧邻时间随机环境下可逗留随机游动的有关性质

给出了可数状态空间中时间随机环境下可逗留随机游动的一个统一模型,对于一维紧邻时间随机环境下的随机游动,在一定的条件下,讨论它的极限性质和中心极限定理,该结论类似于空间随机环境下的随机游动的有关结论.     

Differentiability of the Arrival Time

For a monotonically advancing front, the arrival time is the time when the front reaches a given point. We show that it is twice differentiable everywhere with uniformly bounded second derivative. It is smooth away from the critical points where the equation is degenerate. We also show that the critical set has finite codimensional 2 Hausdorff measure. For a monotonically advancing front, the arrival time is equivalent to the level set method, a~priori not even differentiable but only satisfying the equation in the viscosity sense . Using that it is twice differentiable and that we can identify the Hessian at critical points, we show that it satisfies the equation in the classical sense. The arrival time has a game theoretic interpretation. For the linear heat equation, there is a game theoretic interpretation that relates to Black‐Scholes option pricing. From variations of the Sard and ?ojasiewicz theorems, we relate differentiability to whether singularities all occur at only finitely many times for flows.© 2016 Wiley Periodicals, Inc.     

可压Navier-Stokes方程真空状态的动力学行为

本文主要考虑了一维可压Navier-Stokes方程真空状态的动力学行为.对于任意的熵弱解,如果初始状态不存在真空,我们证明了密度函数关于时间和空间变量是连续的且对于任意时间它是处处为正的.同时,我们还得到了含有间断连接的真空状态的整体熵弱解的存在性,结果显示其真空区域以代数速率被压缩,并在有限时间内消失.     

On the empirical scaling of running time for finding optimal solutions to the TSP

We study the empirical scaling of the running time required by state-of-the-art exact and inexact TSP algorithms for finding optimal solutions to Euclidean TSP instances as a function of instance size. In particular, we use a recently introduced statistical approach to obtain scaling models from observed performance data and to assess the accuracy of these models. For Concorde, the long-standing state-of-the-art exact TSP solver, we compare the scaling of the running time until an optimal solution is first encountered (the finding time) and that of the overall running time, which adds to the finding time the additional time needed to complete the proof of optimality. For two state-of-the-art inexact TSP solvers, LKH and EAX, we compare the scaling of their running time for finding an optimal solution to a given instance; we also compare the resulting models to that for the scaling of Concorde’s finding time, presenting evidence that both inexact TSP solvers show significantly better scaling behaviour than Concorde.     

Distribution Function of the Blow up Time of the Solution of an Anticipating Random Fatigue Equation

In this paper, we study the distribution function of the time of explosion of a stochastic differential equation modeling the length of the dominant crack due to fatigue.The main novelty is that initial condition is regarded as an anticipating random variable and the stochastic integral is in the forward sense.Under suitable conditions, we use the substitution formula from Russo and Vallois to find the local solution of this equation.Then, we find the law of blow up time by proving some results on barrier crossing probabilities of Brownian bridge.     

On the completion time of a job processed on an unreliable machine

1. IntroductionConsider a job processed on an unreIiabIe machine with service repetition. If a job isbeing processed at the instant of machine failure, the service is interrupted, and is restartedanew when the machine is recovered. Let {Xn}, {yn} and {Tn} be mutually independentsequences of independeni identically distributed (i.i.d.) random variables, representing thelifetimes, the repair times of the machine and the service times of the job, respectively. LetZ denote the completion time of…     

数据预处理对替代数据检验方法的影响

替代数据检验法是检验时间序列中是否存在确定性非线性成分的重要统计方法.通过研究差分和数据平滑运算对替代数据检验方法的影响,指出常用的线性滤波等数据预处理步骤破坏了序列的静态性质,从而会导致对零假设的错误拒绝.因此,建议应该直接利用原始时间序列而非应用了差分等非静态滤波运算后的时间序列生成替代数据,再进行假设检验,以免造成对零假设的错误拒绝.     

Jitter analysis of an MMPP-2 tagged stream in the presence of an MMPP-2 background stream

We first consider a single-server queue that serves a tagged MMPP-2 stream and a background MMPP-2 stream in a FIFO manner. The service time is exponentially distributed. For this queueing system, we obtain the CDF of the tagged inter-departure time, from which we can calculate the jitter, defined as a percentile of the inter-departure time. The formulation is exact, but the solution is obtained numerically, which introduces an error that has been found to be negligible. Subsequently, we consider a tandem queueing network consisting of N tandem queues, which is traversed by the MMPP-2 tagged stream, and where each queue also serves a local MMPP-2 background stream. For this queueing network, we obtain an upper bound on the CDF of the inter-departure time from the Nth queue using a heavy traffic approximation, and we verify it by simulation.     

On the Quasi-regularity of Semi-Dirichlet Forms

We prove that if a right Markov process is associated with a semi-Dirichlet form, then the form is necessarily quasi-regular. As applications, we develop the theory of Revuz measures in the semi-Dirichlet context and we show that quasi-regularity is invariant with respect to time change.     

Scheduling data transfers in a network and the set scheduling problem

In this paper we consider the online ftp problem. The goal is to service a sequence of file transfer requests given bandwidth constraints of the underlying communication network. The main result of the paper is a technique that leads to algorithms that optimize several natural metrics, such as max-stretch, total flow time, max flow time, and total completion time. In particular, we show how to achieve optimum total flow time and optimum max-stretch if we increase the capacity of the underlying network by a logarithmic factor. We show that the resource augmentation is necessary by proving polynomial lower bounds on the max-stretch and total flow time for the case where online and offline algorithms are using same-capacity edges. Moreover, we also give polylogarithmic lower bounds on the resource augmentation factor necessary in order to keep the total flow time and max-stretch within a constant factor of optimum.     

A remark on the finite time singularity of the heat flow for harmonic maps

In this paper we study the finite time singularities for the solution of the heat flow for harmonic maps. We derive a gradient estimate for the solution across a finite time singularity. In particular, we find that the solution is asymptotically radial around the isolated singular point in space at a finite singular time. It would be more desirable to understand whether the solution is continuous in space at a finite singular time.Received: 15 March 2001, Accepted: 16 June 2002, Published online: 17 December 2002